Download AHSAA Homeschool Student Eligibility Exams Math Grade 8 Blueprint

AHSAA Homeschool Student Eligibility Exams
Mathematics – Grade 8
Standard
Reference
8.NS
8.NS.1
8.NS.2
8.EE
8.EE.3
8.EE.4
8.EE.5
8.EE.6
Standard Text
The Number System, Expressions and Equations
The Number System
Know that there are numbers that are not rational, and approximate them
by rational numbers.
Know that numbers that are not rational are called irrational. Understand
informally that every number has a decimal expansion; for rational
numbers show that the decimal expansion repeats eventually, and convert
a decimal expansion which repeats eventually into a rational number. [8NS1]
Use rational approximations of irrational numbers to compare the size of
irrational numbers, locate them approximately on a number line diagram,
and estimate the value of expressions (e.g., pi ²). [8-NS2]
Example: By truncating the decimal expansion of (the square root of) 2,
show that (the square root of) 2 is between 1 and 2, then between 1.4 and
1.5, and explain how to continue on to get better approximations.
Expressions and Equations
Work with radicals and integer exponents.
Know and apply the properties of integer exponents to generate
equivalent numerical expressions. [8-EE1]
Example: 32 × 3-5 = 3-3 = 1/33 = 1/27.
Use square root and cube root symbols to represent solutions to equations
of the form x² = p and x³ = p, where p is a positive rational number.
Evaluate square roots of small perfect squares and cube roots of small
perfect cubes. Know that the square root of 2 is irrational. [8-EE2]
Use numbers expressed in the form of a single digit times an integer power
of 10 to estimate very large or very small quantities, and to express how
many times as much one is than the other. [8-EE3]
Example: Estimate the population of the United States as 3 × 108 and the
population of the world as 7 × 109, and determine that the world
population is more than 20 times larger.
Perform operations with numbers expressed in scientific notation,
including problems where both decimal and scientific notation are used.
Use scientific notation and choose units of appropriate size for
measurements of very large or very small quantities (e.g., use millimeters
per year for seafloor spreading). Interpret scientific notation that has been
generated by technology. [8-EE4]
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Percentage
of Test
Items
40%
Page 1
Standard
Reference
8.EE.7
8.EE.8
8.EE.9
8.EE.9.a
8.EE.9.b
8.EE.10
8.EE.10.a
8.EE.10.b
8.EE.10.c
Standard Text
Percentage
of Test
Items
Understand the connections between proportional relationships, lines, and
linear equations.
Graph proportional relationships, interpreting the unit rate as the slope of
the graph. Compare two different proportional relationships represented
in different ways. [8-EE5]
Example: Compare a distance-time graph to a distance-time equation to
determine which of two moving objects has greater speed.
Use similar triangles to explain why the slope m is the same between any
two distinct points on a non-vertical line in the coordinate plane; derive the
equation y = mx for a line through the origin and the equation y = mx + b
for a line intercepting the vertical axis at b. [8-EE6]
Analyze and solve linear equations and pairs of simultaneous linear
equations.
Solve linear equations in one variable. [8-EE7]
Give examples of linear equations in one variable with one solution,
infinitely many solutions, or no solutions. Show which of these possibilities
is the case by successively transforming the given equation into simpler
forms, until an equivalent equation of the form x = a, a = a, or a = b results
(where a and b are different numbers). [8-EE7a]
Solve linear equations with rational number coefficients, including
equations whose solutions require expanding expressions using the
distributive property and collecting like terms. [8-EE7b]
Analyze and solve pairs of simultaneous linear equations. [8-EE8]
Understand that solutions to a system of two linear equations in two
variables correspond to points of intersection of their graphs, because
points of intersection satisfy both equations simultaneously. [8-EE8a]
Solve systems of two linear equations in two variables algebraically, and
estimate solutions by graphing the equations. Solve simple cases by
inspection. [8-EE8b]
Example: 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y
cannot simultaneously be 5 and 6.
Solve real-world and mathematical problems leading to two linear
equations in two variables. [8-EE8c]
Example: Given coordinates for two pairs of points, determine whether the
line through the first pair of points intersects the line through the second
pair.
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Page 2
Standard
Reference
8.F
8.F.11
8.F.12
8.F.13
8.F.14
8.F.15
8.G
8.G.16
8.G.16.a
8.G.16.b
8.G.16.c
8.G.17
Standard Text
Functions
Define, evaluate, and compare functions.
Understand that a function is a rule that assigns to each input exactly one
output. The graph of a function is the set of ordered pairs consisting of an
input and the corresponding output. (Function notation is not required in
Grade 8.) [8-F1]
Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions).
[8-F2]
Example: Given a linear function represented by a table of values and
linear function represented by an algebraic expression, determine which
function has the greater rate of change.
Interpret the equation y = mx + b as defining a linear function, whose graph
is a straight line; give examples of functions that are not linear. [8-F3]
Example: The function A = s2 giving the area of a square as a function of its
side length is not linear because its graph contains the points (1,1), (2,4),
and (3,9), which are not on a straight line.
Use functions to model relationships between quantities.
Construct a function to model a linear relationship between two quantities.
Determine the rate of change and initial value of the function from a
description of a relationship or from two (x, y) values, including reading
these from a table or from a graph. Interpret the rate of change and initial
value of a linear function in terms of the situation it models, and in terms
of its graph or a table of values. [8-F4]
Describe qualitatively the functional relationship between two quantities
by analyzing a graph (e.g., where the function is increasing or decreasing,
linear or nonlinear). Sketch a graph that exhibits the qualitative features of
a function that has been described verbally. [8-F5]
Geometry, Statistics and Probability
Geometry
Understand congruence and similarity using physical models,
transparencies, or geometry software.
Verify experimentally the properties of rotations, reflections, and
translations: [8-G1]
Lines are taken to lines, and line segments to line segments of the same
length. [8-G1a]
Angles are taken to angles of the same measure. [8-G1b]
Parallel lines are taken to parallel lines. [8-G1c]
Understand that a two-dimensional figure is congruent to another if the
second can be obtained from the first by a sequence of rotations,
reflections, and translations; given two congruent figures, describe a
sequence that exhibits the congruence between them. [8-G2]
© 2016 Scantron Corporation. All rights reserved.
Percentage
of Test
Items
31%
29%
Page 3
Standard
Reference
8.G.18
8.G.19
8.G.20
8.G.21
8.G.22
8.G.23
8.G.24
8.SP
8.SP.25
8.SP.26
Standard Text
Percentage
of Test
Items
Describe the effect of dilations, translations, rotations, and reflections on
two-dimensional figures using coordinates. [8-G3]
Understand that a two-dimensional figure is similar to another if the
second can be obtained from the first by a sequence of rotations,
reflections, translations, and dilations; given two similar two-dimensional
figures, describe a sequence that exhibits the similarity between them. [8G4]
Use informal arguments to establish facts about the angle sum and exterior
angle of triangles, about the angles created when parallel lines are cut by a
transversal, and the angle-angle criterion for similarity of triangles. [8-G5]
Example: Arrange three copies of the same triangle so that the sum of the
three angles appears to form a line, and give argument in terms of
transversals why this is so.
Understand and apply the Pythagorean Theorem.
Explain a proof of the Pythagorean Theorem and its converse. [8-G6]
Apply the Pythagorean Theorem to determine unknown side lengths in
right triangles in real-world and mathematical problems in two and three
dimensions. [8-G7]
Apply the Pythagorean Theorem to find the distance between two points in
a coordinate system. [8-G8]
Solve real-world and mathematical problems involving volume of cylinders,
cones, and spheres.
Know the formulas for the volumes of cones, cylinders, and spheres and
use them to solve real-world and mathematical problems. [8-G9]
Statistics and Probability
Investigate patterns of association in bivariate data.
Construct and interpret scatter plots for bivariate measurement data to
investigate patterns of association between two quantities. Describe
patterns such as clustering, outliers, positive or negative association, linear
association, and nonlinear association. [8-SP1]
Know that straight lines are widely used to model relationships between
two quantitative variables. For scatter plots that suggest a linear
association, informally fit a straight line, and informally assess the model fit
by judging the closeness of the data points to the line. [8-SP2]
© 2016 Scantron Corporation. All rights reserved.
Page 4
Standard
Reference
8.SP.27
8.SP.28
Standard Text
Percentage
of Test
Items
Use the equation of a linear model to solve problems in the context of
bivariate measurement data, interpreting the slope and intercept. [8-SP3]
Example: In a linear model for a biology experiment, interpret a slope of
1.5 cm/hr as meaning that an additional hour of sunlight each day is
associated with an additional 1.5 cm in mature plant height.
Understand that patterns of association can also be seen in bivariate
categorical data by displaying frequencies and relative frequencies in a
two-way table. Construct and interpret a two-way table summarizing data
on two categorical variables collected from the same subjects. Use relative
frequencies calculated for rows or columns to describe possible association
between the two variables. [8-SP4]
Example: Collect data from students in your class on whether or not they
have a curfew on school nights, and whether or not they have assigned
chores at home. Is there evidence that those who have a curfew also tend
to have chores?
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